The dynamic system method and the traps

1 March 1998

journal article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 30 (1) , 137-151
https://doi.org/10.1239/aap/1035227996

Abstract

We transpose the ordinary differential equation method (used for decreasing stepsize stochastic algorithms) to a dynamical system method to study dynamical systems disturbed by a noise decreasing to zero. We prove that such an algorithm does not fall into a regular trap if the noise is exciting in an unstable direction.

Keywords

This publication has 11 references indexed in Scilit:

Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method
Advances in Applied Probability, 1996
General results on the convergence of stochastic algorithms
IEEE Transactions on Automatic Control, 1996
A Dynamical System Approach to Stochastic Approximations
SIAM Journal on Control and Optimization, 1996
Random perturbations of recursive sequences with an application to an epidemic model
Journal of Applied Probability, 1995
Chain recurrence in surface flows
Discrete & Continuous Dynamical Systems, 1995
Almost sure convergence of a class of stochastic algorithms
Stochastic Processes and their Applications, 1994
A stochastic approximation type EM algorithm for the mixture problem
Stochastics and Stochastic Reports, 1992
Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
Stochastic Processes and their Applications, 1987
Analysis of recursive stochastic algorithms
IEEE Transactions on Automatic Control, 1977
Limit theorems for stochastic growth models. I
Advances in Applied Probability, 1972